Abstract
Spin transport theory of non-Hermitian quantum systems, where the non-Hermiticity led to a series of exotic phenomena when the system experiences dissipation to an environment is proposed. The goal is a better understanding of the spin diffusion in the one-dimensional non-Hermitian XXZ model which allows the transport coefficients be computed analytically. Moreover, we analyzed the electric transport in the one-dimensional non-Hermitian Hubbard model which is a very important model of electrons strongly correlated, where we have investigated the effect of non-Hermitian parameters like the imaginary hopping on AC and DC conductivities of the system. We analyzed the large U limit of this model, where such non-Hermiticity contributes with a minus sign in the virtual exchange of quasiparticles and the behavior of the ground state energy and low-lying excitations is reversed.